Harrison does rip through those movements. I have a few of the CDs that Pearl issued of Elgar conducting his own works and I'm surprised at how fast he conducts a lot of the pieces. It wouldn't surprise me if he did this just so they fit correctly on record, but he could have also preferred the tempos. The recordings are really great to listen to if you want to hear the style of English orchestras from the first half of the 20th century. My favorite part is how much they used to slide between notes and how they planned these slides within phrases "tastefully".
But I think you'll find the same thing in a number of older recordings. Take anything recorded by Albert Coates, for instance - his tempos are often blazingly fast, and yet there's often a degree of fine articulation you don't hear in some of today's more homogenized performances. There is of course always the suspicion that decisions on tempos, cuts, repeats, etc., were motivated by the length of the 78 rpm side. Weingartner's Beethoven 7th, for example, which leaves out almost all repeats, was timed I'm sure to fit on 9 78 rpm sides. I don't recall offhand if Elgar assigned metronome markings to his works, but I think you'll find that many modern performances of orchestral music come out far slower than the composer's markings. For example, Tchaikovsky's setting for the opening Allegro of the 5th symphony, dotted quarter = 104, is faster than any modern performance I have ever heard, where dotted quarter = 72 is not uncommon. The portamentos you speak of are also largely gone today. You can still hear them in Toscanini's 1938 Eroica (I forget which orchestra), but by his last recording around 1950 with the NBC they're gone.
I realize there are a lot of holes to pick in all the above, but I'm just writing it very quickly OTTOMH, and at 60 wpm.